On the Causality and K-Causality between Measures
نویسندگان
چکیده
Drawing from the optimal transport theory adapted to the Lorentzian setting, we propose and study the extension of the Sorkin–Woolgar causal relation K+ onto the space of Borel probability measures on a given spacetime. We show that it retains its fundamental properties of transitivity and closedness. Furthermore, we list and prove several characterizations of this relation, including the “measure-theoretic” analogue of the characterization of K+ in terms of time functions.
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